The art of the present invention relates to board games in general and more particularly to a horse racing board game having a track with a plurality of numbered lanes in which each lane is divided into positions, spaces, or segments. For the preferred embodiment, the number of positions, spaces, or segments per lane is substantially proportional to the relative probability of a pair of conventional dice rolling the lane number on a single roll.
It is recognized within and during the play of games which utilize a pair of dice that the minimum value which may be rolled per pair is 2 (i.e. two ones) and the maximum value which may be rolled is twelve (i.e. two sixes). It is also recognized that the probability of rolling a seven on a single roll of two dice is greater than that of any other value. For a value of two or of 12 to occur during a single roll, the probability is easily calculated as:
          ⁢                    1        6            ·              1        6              =          1      36      That is, since each dice is six sided and two ones or two sixes must be rolled at the same time respectively, the total probability is the product of each single value dice probability. When calculating the probability of other values occurring, the permutations and combinations of such occurrence must be contemplated prior to calculation of the probability. For example, the probability of rolling a seven value is the summation of the probabilities of rolling the combination of a one-six, a two-five, a three-four, a four-three, a five-two, and a six-one. Each of the corresponding individual values represents a probability of 1/36 and when summed represent:
          ⁢                    1        6            +              1        6            +              1        6            +              1        6            +              1        6            +              1        6              =                  6        36            =              1        6            So while the probability of rolling a two or a 12 value is 1/36, the probability of rolling a seven is much greater at ⅙. When calculated for all values which may be rolled from a pair of dice, the following table represents the respective probabilities:
Value23456789101112Probability1/362/363/364/365/366/365/364/363/362/361/36
Thus, if movement of a game piece is dependent upon the lane number which a pair of dice rolls, the number of spaces or segments for each lane must represent the probabilities of rolling that lane number in order to provide a substantially equal chance of each game piece in each lane crossing the finish line. If each lane had the same number of spaces or segments and every time the lane number was rolled with a pair of dice, the game piece in that lane advanced one space, lane seven would most likely win every game. In order to make the probabilities of each lane winning approximately equal with the other lanes, the number of spaces per lane must substantially satisfy the following equation:
          ⁢            (              number        ⁢                                  ⁢        of        ⁢                                  ⁢        spaces        ⁢                                  ⁢        per        ⁢                                  ⁢        lane        ⁢                                  ⁢        for        ⁢                                  ⁢        X            )        =                  ⁢          n      ·      36      ·              (                  probability          ⁢                                          ⁢          of          ⁢                                          ⁢          rolling          ⁢                                          ⁢          the          ⁢                                          ⁢                                          ⁢          lane          ⁢                                          ⁢          number          ⁢                                          ⁢          X          ⁢                                          ⁢          with          ⁢                                          ⁢          a          ⁢                                          ⁢          single          ⁢                                          ⁢          roll          ⁢                                          ⁢          of          ⁢                                          ⁢          a          ⁢                                          ⁢          pair          ⁢                                          ⁢          of          ⁢                                          ⁢          dice                )            Where “n” is an integer value greater than zero. If the aforesaid equation is not satisfied for each lane, one or more lanes will have an advantage or disadvantage relative to the other lanes.
Prior art board games and horse racing board games in particular which utilize a pair of dice for game piece movement have failed to account for the aforesaid. That is, they generally treat a roll of a pair of dice as a random number generator. From the aforesaid, it is clear that the value rolled from a pair of dice is not a uniform probabilistic distribution. This phenomena forces each player to roll the dice for each lane rather than the game as a whole. This prior art technique of play is further described in U.S. Pat. No. 5,226,655, entitled Apparatus and Method of Playing a Board Game Simulating Horse Racing and Wagering issued to Rickabaugh on Jul. 13th, 1993.
In its preferred embodiment, the present art comprises a game board having eleven lanes numbered two through 12 and a holding stable for game pieces (preferably in the form of horses) corresponding to lanes which are not utilized within the game. The game pieces corresponding to the lane numbers which are not utilized are placed within the holding stable substantially adjacent to a currency amount which must be paid into a central game pot if a player rolls a value corresponding to the lane number of a game piece not running the race. In its preferred embodiment, the present art utilizes a pair of dice which, when rolled, allow the players to move the game piece in the lane corresponding to the value which occurs due to the dice roll yet graduates the number or amount of spaces or positions per numbered lane in order to substantially equalize the probabilities of any game piece crossing the finish line. For the preferred embodiment, the number of spaces or positions for each lane prior to the finish line is:
Lane Number23456789101112Number of spaces or 24681012108642positionsFor the preferred embodiment, probabilistically, the total number of spaces or segments per lane prior to the finish line is an integer number which substantially represents the theoretical number of times the lane number would occur (i.e. be rolled by the dice) if a pair of dice were rolled 72 times. The preferred embodiment of the present art game has a fiat game currency denominated as 1, 2, 3, 5, & 10 which is used during game play. A set of playing cards numbered two through 12 which correspond to the relative lane numbers are randomly distributed to the players with the exception of the card values retained within the holding stable. The players holding the card numbers corresponding to the lane number in which a game piece first crosses the finish line divide and retain the game currency within the pot.
Accordingly, it is an object of the present invention to provide a horse racing board game which allows each player to hold numbered cards which collectively represent the player's proportional stake of the pot for the game piece horse within the lane which crosses the finish line first.
Another object of the present invention is to provide a horse racing board game utilizing the random nature of a dice roll for all game piece movement yet giving each player holding a stake in any particular lane number a substantially equal chance of winning the game currency within a central game pot.
A further object of the present invention is to provide a horse racing board game having a plurality of numbered lanes corresponding to the values which can occur from a single roll of a pair of dice.
A yet further object of the present invention is to provide a horse racing board game having a number of spaces or segments per numbered lane which substantially equalizes the probability that any player holding cards of any numbered lane will win a stake in the game pot upon final crossing of the finish line by any game piece.
A still further object of the present invention is to provide a horse racing board game which allows each player to have a stake in the game as a whole rather than any individual game piece.